Algorithms and experiments around Dehn surgery and the census L-space knots

• Applicant: Dr. Marc Kegel
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 561898308

My guiding motivation in this proposal is to understand in which ways 3-manifolds arise as Dehn surgeries on knots, in particular, I want to understand L-space knots. I would like to find a topological characterization of L-space knots and understand their relation to hyperbolic geometry. For that, I will algorithmically and theoretically deeply analyze Dunfield's census knots, the hyperbolic knots with the simplest complements. It turns out that approximately half of them are L-space knots and some more are fibered and induce the standard tight contact structure. This suggests a relation between contact geometry and Heegaard Floer homology on the one side and hyperbolic geometry on the other side that is not yet understood. I also plan to study related algorithmic questions and projects in knot theory, the theory of Dehn surgery, and contact geometry.

• DFG Programme: Research Grants